Quasi-Periodic Breathers of the Hirota-Maccari System

N-soliton solutions for the [formula omitted]-dimensional Hirota–Maccari equation in fluids, plasmas and optical fibers

A number of two-dimensional fluid models in geophysical fluid dynamics and plasma physics are examined to find out whether they have steady and localized monopole vortex solutions. A simple and general method that consists of two steps is used. First the dispersion relation is calculated, to find all possible values of the phase velocity of the linear waves. Then an integral relation that determines the center-of-mass velocity of localized structures must be found. The existence condition is that this velocity should be outside the region of linear phase velocities. After a presentation of the method, previous work on the plasma drift wave model and the shallow-water equations is reviewed. In both cases it is found that the center-of-mass velocity is larger than the maximum phase velocity of the linear waves if the amplitude is large enough, and steady localized vortices can therefore exist. New results are then obtained for a number of two-field models. For the coupled ion acoustic-drift modes in plasmas, it is found that the center-of-mass velocity depends on the ratio between the parallel ion velocity component and the electrostatic potential in the vortex. If this ratio is large enough, the vortex can be steady. For the drift-Alfven mode the "center-of-charge" velocity is proportional to the ratio between the parallel current and the total charge in the vortex. It can therefore be steady if this ratio satisfies the appropriate conditions. For the quasigeostrophic two-layer equations, describing stratified flow on a rotating planet, it is found that the center-of-mass velocity is determined by the ratio between the baroclinic and the barotropic components in the vortex. If a baroclinic component with an appropriate sign is added to a barotropic vortex, it propagates faster than the barotropic Rossby waves, and can be steady. Finally, the existence conditions for a vortex in an external zonal flow are examined. It is found that the center-of-mass velocity acquires an additional westward contribution in an anticyclonic shear zone in the framework of the shallow-water equations, and also that an easterly jet south of this shear zone partly shields a vortex situated in the shear zone from the dispersive influence of the fast Rossby waves on the equatorward side.

The work presented in this paper estimates the spectral radiance emitted from plasma induced by the interaction of hypervelocity moving structural/material systems with the atmosphere. The motivation for this effort originates from the need to compute the radiative heat fluxes imparted to hypersonic vehicles to facilitate their design, control, and maintenance. In response to this need, a computational framework was established to predict the fluid dynamics fields around a hypervelocity vehicle that in turn is coupled with the plasma physics that enables the calculation of the plasma fields and species dynamics. This framework implements a one-way coupling between fluid dynamics and plasma physics models. The framework solves the fluid dynamics partial differential equations representing the conservation of mass, momentum, and energy. The computed pressure, velocity, and temperature fields are subsequently utilized to drive the plasma physics PDEs describing the mass transport and energetics of all the nitrogen-oxygen 11 species present according to the so-called Dunn plasma model. An application of this framework for a spherical body for a wide range of velocities is presented as a verification of the framework’s functionality. Typical distributions of the fluid and plasma dynamics are presented. Finally, the plasma radiance spectra are produced by employing statistical mechanics principles.

Quasi-periodic breathers and their dynamics to the Fokas system in nonlinear optics

A unified concatenation model for plasma physics: Integrability and soliton solutions

By using the reductive perturbation technique, the nonlinear dust ion-acoustic solitary wave models of the damped Korteweg–de Vries (D-KdV) and modified damped Korteweg–de Vries (D-mKdV) equations are formulated. We constructed the more general and new solitary wave solutions of nonlinear damped KdV and damped mKdV equations by using the modified mathematical technique. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of adiabatic parameters, dynamics of fluid and problems of biomedical, industrial phenomena. The new solutions are obtained in the shape of dark solitons, bright solitons, traveling wave and kink and anti-kink wave solitons. We show the physical structure of new solutions by two and three-dimensions graphical to know the physical interpretation of different structure of dust ion-acoustic solitary wave. The calculations show that this new technique is more powerful, effective, straightforward, and fruitfulness to study analytically other nonlinear complex physical models in plasma physics, mathematical physics, fluid mechanics, hydrodynamics, mathematical biology and many other physical sciences.

This paper retrieves the investigation of rational solitons via symbolic computation with logarithmic transformation and ansatz functions approach for the [Formula: see text]-dimensional generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt (GKDKK) equation in fluid mechanics, ocean dynamics and plasma physics. We find two categories of M-shaped rational solitons and their dynamics will be revealed through graphs by choosing the suitable values of involved parameters. In addition, two categories of M-shaped rational solitons and their interactions with kink waves will be analyzed. Furthermore, homoclinic breathers, multi-wave and kink cross rational solitons will be investigated. The periodic, rational, dark, bright, Weierstrass elliptic function and positive soliton solutions will also be retrieved with the aid of Sub-ODE approach. Moreover, stability characteristics of solutions will be evaluated.

Single-track laser fusion were simulated using a heat-transfer-solidification-only (HTS) model and its extension with fluid dynamics (HTS_FD) model using a parallel open-source code, which included laminar fluid dynamics, flat-free surface of the molten alloy, heat transfer, phase-change, evaporation, and surface tension phenomena. The results illustrate that the fluid dynamics affects the solidification and ensuing microstructure. For the HTS_FD simulations, thermal gradient, G was found to exhibit a maximum at the extremity of the solidified pool (i.e., at the free surface), while for HTS simulations, G exhibited a maximum around the entire edge of the solidified pool. HTS_FD simulations predicted a wider range of cooling rates than the HTS simulations, exhibited an increased spread in the solidification speed, V variation within the melt-pool with respect to the HTS model results. Primary dendrite arm spacing (PDAS) were evaluated based on power law correlations and marginal stability theory models using the (G, V) from HTS and HTS_FD simulations to quantify the effect of the fluid dynamics on the microstructure. At low-laser powers and low-scan speeds, the PDAS obtained with the fluid dynamics model (HTS_FD) was larger by more than 30 pct with respect to the PDAS calculated with the simple HTS model. A new PDAS correlation, i.e., lambda_{1} left[ {mu {text{m}}} right] = 832;Gleft[ {text{K/m}} right]^{ - 0.5} Vleft[ {text{m/s}} right]^{ - 0.25} , which uses the (G, V) results from the HTS_FD model was developed and validated against experimental results.

In this paper, by combining the direct method proposed by Nakamura with the numerical algorithms, the N-periodic wave solutions of two kinds of (2+1)-dimensional KdV-type equations are investigated, which are applied in fluid dynamics and plasma physics. The problem of solving N-periodic wave solutions can be transformed into a least squares problem and addressed by using numerical algorithms. The three- and four-periodic wave solutions of the KdV-type equations are obtained and some numerical results are presented. It is verified that the N-periodic wave solutions approach to the N-soliton solutions under a small amplitude limit. The dynamic behaviors of the quasi-periodic wave solutions are analyzed by utilizing the characteristic lines. The numerical procedure adopted in this paper can be further generalized to other high-dimensional nonlinear integrable systems.

In this study, we investigate the soliton dynamics and stability properties of the time-fractional Hamiltonian amplitude (FHA) equation using the improved F-expansion method. The FHA equation, a fractional extension of the nonlinear Schrödinger equation, governs a wide range of nonlinear physical phenomena, including plasma physics, fluid dynamics, and optical communications. We exploit the beta fractional derivative approach to explore soliton solutions, chaotic behavior, bifurcations, and sensitivity analysis of the model parameters. The attained results reveal a variety of soliton structures, such as quasiperiodic, anti-peakon, and multi-periodic solitons, which are graphically represented to highlight their physical significance. Stability analysis using the linear stability method confirms the robustness of these solutions under certain perturbations. Moreover, bifurcation analysis via phase plane diagrams exposes key insights into the qualitative changes in the dynamical system, including the presence of quasiperiodic and chaotic behavior under external perturbations. These findings contribute to a deeper understanding of complex nonlinear systems and have potential applications in signal processing, optical fiber communications, and materials science.

The work herein presents an effort to compute the spectral radiance emitted from plasma induced by the interaction of hypervelocity moving structural/material systems with the atmospheres. The motivation for this effort originates from the need to compute the radiative heat fluxes imparted to hypersonic vehicles in order to enhance their design, control, and maintenance. In response to this need, a computational framework is established to predict the fluid dynamics fields around a hypervelocity vehicle. The framework is one-way coupled with an appropriate plasma physics model, that enables the calculation of the plasma fields and plasma species dynamics. The framework is configured first to solve the fluid dynamics partial differential equations representing the conservation of mass, momentum, and energy under steady-state conditions. The computed pressure, velocity, and temperature fields are subsequently utilized to drive the plasma physics partial differential equations describing the mass transport and energetics of all the species present according to the Dunn plasma model. An application of this framework for a spherical body in a wide range of initial velocities is presented to verify the framework's functionality. Typical distributions of the fluid and plasma dynamics are presented. Finally, the plasma spectral radiance distributions are produced by employing statistical mechanics principles and the high-resolution transmission molecular absorption database.

Modeling of fluid dynamics and the associated heat transfer induced by plasma between two parallel electrodes is investigated. In particular, we consider a capacitvely coupled radio frequency discharge plasma generator, where the plasma is generated on the surface of a dielectric circuit board with electrode strips on the top and bottom. The electrodes have a thickness of 100 μm, which is comparable to the height of the boundary layer. The regime considered is that the electron component is in the non-equilibrium state, and the plasma is nonthermal. Overall, due to the ion and large fluid particle interaction, the pressure is higher in the downstream of the electrode, causing the velocity structure to resemble that of a wall jet. Parameters related to the electrode operation, including the voltage, frequency, and free stream speed are varied to investigate the characteristics of the plasma-induced flow. Consistent with the experimental observation, the model shows a clear dependence of the induced jet velocity on the applied voltage and frequency. The heat flux exhibited a similar dependence on the strength of the plasma. The present plasma-induced flow concept can be useful for thermal management and active flow control.

Development of three-dimensional capabilities for modelling stationary fluctuations in nuclear reactor cores

This article analyzes the analytic and solitary wave solutions of the one-dimensional Zabolotskaya-Khokholov (ZK) dynamical model which provides information about the propagation of sound beam or confined wave beam in nonlinear media and studies of beam deformation. By the Lie symmetry analysis method, we acquire the vector fields, commutation relations, optimal system, reduction, and analytic solutions to the specified equation by exerting the Lie group method. Moreover, the solitary wave solutions of the ZK model are procured by exerting the new auxiliary equation method (NAEM). The behavior of the acquired outcomes for several cases is exhibited graphically through two and three-dimensional dynamical wave profiles. Furthermore, the conservation laws of the ZK model are acquired by Ibragimov’s new conservation theorem.

Analysis of beam propagation, kinetic and fluid dynamic processes in Cs diode pumped alkali lasers (DPALs), using wave optics model and gasdynamic code, is reported. The analysis is based on a three-dimensional, time-dependent computational fluid dynamics (3D CFD) model. The Navier-Stokes equations for momentum, heat and mass transfer are solved by a commercial Ansys FLUENT solver based on the finite volume discretization technique. The CFD code which solves the gas conservation equations includes effects of natural convection and temperature diffusion of the species in the DPAL mixture. The DPAL kinetic processes in the Cs/He/C 2 H 6 gas mixture dealt with in this paper involve the three lowest energy levels of Cs, (1) 6 2 S 1/2 , (2) 6 2 P 1/2 and (3) 6 2 P 3/2 . The kinetic processes include absorption due to the 1→3 D 2 transition followed by relaxation the 3 to 2 fine structure levels and stimulated emission due to the 2→1 D 1 transition. Collisional quenching of levels 2 and 3 and spontaneous emission from these levels are also considered. The gas flow conservation equations are coupled to fast-Fourier-transform algorithm for transverse mode propagation to obtain a solution of the scalar paraxial propagation equation for the laser beam. The wave propagation equation is solved by the split-step beam propagation method where the gain and refractive index in the DPAL medium affect the wave amplitude and phase. Using the CFD and beam propagation models, the gas flow pattern and spatial distributions of the pump and laser intensities in the resonator were calculated for end-pumped Cs DPAL. The laser power, DPAL medium temperature and the laser beam quality were calculated as a function of pump power. The results of the theoretical model for laser power were compared to experimental results of Cs DPAL.